Question 393: Current Electricity

Question

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P
1
, P
2
and P
3
respectively, then :

Accepted Answer

We have the following cases :
$$\bullet$$ For configuration (I) : Considering as Wheatstone's bridge, we get the equivalent resistance as $${({R_I})_{eq}} = 1\,\Omega $$.
$$\bullet$$ For configuration (II) : The given configuration is further reduced as follows:
That is, $${({R_{II}})_{eq}} = {1 \over 2}\,\Omega $$.
$$\bullet$$ For configuration (III) : Similarly, we get $${({R_{III}})_{eq}} = 2\,\Omega $$.
The power is given by
$$P = {{{V^2}} \over R}$$
Since V is the same for all three configurations, we have the power as a quantity indirectly proportional to the resistance :
$$P \propto {1 \over R}$$
From the above three case, we have $${({R_I})_{eq}} = 1\,\Omega ;\,{({R_{II}})_{eq}} = {1 \over 2}\,\Omega ;\,{({R_{III}})_{eq}} = 2\,\Omega $$, which implies that
$${R_{II}} > {R_I} > {R_{III}}$$
Therefore, $${P_2} > {P_2} > {P_3}$$

Answer

P
1
>  P
2
>  P
3

Answer

P
1
>  P
3
>  P
2

Answer

P
2
>  P
1
>  P
3

Answer

P
3
>  P
2
>  P
1

Current Electricity

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P 1 , P 2 and P 3 respectively, then :

Choose the correct answer: